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00925njm 22002777a 4500 dc Acquistapace, Francesca author Broglia, Fabrizio author Fernando Galván, José Francisco author 2015-12-17 In this work we present the concept of C-semianalytic subset of a real analytic manifold and more generally of a real analytic space. C-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by Cartan (C-analytic sets for short). More precisely S is a C-semianalytic subset of a real analytic space (X, OX ) if each point of X has a neighborhood U such that S ∩ U is a finite boolean combinations of global analytic equalities and strict inequalities on X. By means of paracompactness C-emianalytic sets are the locally finite unions of finite boolean combinations of global analytic equalities and strict inequalities on X. The family of C-semianalytic sets is closed. 0025-5831 10.1007/s00208-015-1342-5 https://hdl.handle.net/20.500.14352/24309 http://link.springer.com/article/10.1007%2Fs00208-015-1342-5#page-1 http://link.springer.com On globally defined semianalytic sets